Conventionally, the geometric distance is usually computed between two binary masks in terms of L1 or IoU loss [1]}, [2]}, [3]}, [4]}.
However, obtaining the mask of the reconstructed mesh usually involves rasterization that discretizes the mesh into a grid of pixels. This operation inevitably introduces information loss and thus inaccurate supervision signals.
This is particularly harmful to a well-trained ConvMesh, the shape manifold of which is typically smooth.
Specifically, a small perturbation in \(\mathbf {z}\)  usually corresponds to a slight variation in the 3D shape, which may translate to an unchanged binary mask.
This usually leads to an insensitive gradient for back-propagation, which undermines geometric learning. We analyze the sensitivity of existing losses in the experiment.
